On smoothing properties of compound Poisson distributions (Q1925159)

The main contributions are estimates of analogs of the uniform Kolmogorov distance and Lévy concentration function of products of terms of the type \((F-E)^k\exp[a(F-E)]\), where products and powers are in the convolution sense, \(F\) is a distribution function and \(E\) is the distribution concentrated at zero. Some applications to sums of a random number of random variables are also given.